Off-spinner Dilruwan Perera and Rangana Herath combined forces to dismantle the Australian batting in both the innings as the hosts took an unassailable 2-0 lead in the three-match series.
Perera, Herath lead Sri Lanka to series win over Australia
Perera bagged six wickets to help bundle out Australia for 183 after lunch on the third day as Sri Lanka registered their first Test series triumph against the visitors since 1999.
Herath set up the win for the hosts with his maiden Test hat-trick which helped dismiss Australia for a record low of 106 in their first innings.
Australia faltered in their second outing as well after Perera, who registered his career-best figures of 6-70, sent the visitors packing in just 50.1 overs as the Sri Lankan players went into a celebratory huddle.
"It feels great. The way we played in the last two games, I thought we were brilliant. To beat the number one team is very satisfying," Sri Lankan skipper Angelo Mathews told reporters.
Herath takes hat-trick against Australia
Overnight batsmen David Warner and skipper Steven Smith offered some resistance with their 51-run fourth wicket partnership but both of them fell to Perera's guile.
Warner, who tried to counter attack during his 31-ball 41, was trapped lbw off a straighter Perera delivery that hit the batsman on the front pad.
Smith (30), who used his feet well against the spinners during his 58-ball stay, was the next to go as he gave away a catch at backward short leg.
Man of the match Perera, who bagged 10 wickets in the match, then bowled Adam Voges for 28 to register his fourth five-wicket haul in 11 Test matches.
"They (Australian batsmen) look a bit lost when it comes to our spinners. Our spinners have bowled extremely well. They found it a bit hard to score off our spinners," said Mathews.
But it was Herath's left-arm spin that did the early damage in a match dominated by Sri Lankan slow bowlers.
Herath and Perera shared four wickets between them on a chaotic second day which saw the fall of 21 wickets and put the match on the fast track.
ri Lanka edge day one with Mendis, Mathews’ fifties
The 38-year-old Herath, who became only the second Sri Lankan to claim a hat-trick after former pacer Nuwan Zoysa, dismissed Voges, Peter Nevill and Mitchell Starc off consecutive deliveries.
Australia's pace spearhead Starc though made his presence felt on a track that offered little help to the fast bowlers with his career-best match figures of 11-94.
But Starc's standout show for Australia did little to help the team's dismal record in the sub-continent.
Australia's last outing to the sub-continent saw them lose all four Tests against India in 2013 and they also lost both matches when Pakistan hosted them for a two-Test series in 2014 in the Gulf.
"It's been too long now - I think it's been 15 or 16 games since we've won a game in the sub-continent, so whatever we're doing it's not working," a disappointed Smith said after the loss.
"We have to find ways to score and find ways to take wickets and chase runs. We have not been able to do that in the first two Test matches.
"Credit to Sri Lanka for the way they have played to wrap up series here today," Smith added Saturday.
The action now shifts to Colombo for the final Test beginning August 13.
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